The exponential function that passes through (0,2) and (3,54) is a growth function
The exponetial function is y = 2 * 3^x
<h3>How to construct the exponential function?</h3>
The points are given as:
(x,y) = (0,2) and (3,54)
An exponential function is represented as:
y = ab^x
Substitute the points in the equation
2 = ab^0 and 54 = ab^3
Solve 2 = ab^0
a = 2
Substitute 2 for a in 54 = ab^3
54 = 2b^3
Divide by 2
27 = b^3
Take the cube roots of both sides
b = 3
So, we have:
y = ab^x
This becomes
y = 2 * 3^x
Hence, the exponetial function is y = 2 * 3^x
Read more about exponential functions at:
brainly.com/question/24077767
Two equations for two perpendicular lines that have the same y-intercept and do not pass through the same origin are; y = x + 1 and y = -x + 1
<h3>What is the equation of the two lines?</h3>
The general formula for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, when we talk about two perpendicular lines, it means that their slopes are negative reciprocals of each other.
Secondly, we are told that they both do not pass through the origin. Thus, it means that the y-intercept cannot be zero.
Therefore, two possible equations here can be;
y = x + 1 and y = -x + 1
Read more about Equation of lines at; brainly.com/question/13763238
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We can't find explicit values for 
and 
, since there is only one equation, but two variables.
The best we can do is solve for one variable with respect to the other:
Solve for :
subtract 
from both sides:
divide both sides by 
:
Solve for :
subtract 
from both sides:
divide both sides by 
:
